Dynamic selection of visible wavelengths using resonant TiO₂ nanostructures

2.1 Fabrication

Different PDMS-embedded TiO₂ nanodisc arrays were prepared on quartz substrates. The quartz substrate was cleaned by sonication in acetone and isopropyl alcohol (IPA). The sacrificial germanium oxide layer was formed onto the quartz substrate by depositing a 100 nm-thick Ge layer using an e-beam evaporation system followed by annealing at 600 °C for 10 min under an O₂ gas flow of 1000 sccm. This is a reliable method for fabricating a sacrificial germanium oxide layer. The TiO₂ nanodisc arrays were formed using e-beam lithography followed by ALD deposition. To form the 275 nm thick electron-beam resist layer, a pristine electron-beam resist solution (ZEP520A, Zeon Corp.) was diluted with anisole solvent (99.7 %, Sigma-Aldrich) at a 1:2 volume ratio. The diluted e-beam resist solution was spin-coated onto the germanium oxide layer at a speed of 3000 rpm for 45 s. Subsequently, the substrate was annealed at 180 °C for 3 min. The desired hole pattern was written using e-beam lithography (ELS-125, Elionix) at a dose of 400 μC/cm² and beam current of 1 nA, which produced the hole patterns over a 250 × 250 μm area. The hole diameter was 120 nm, and the pitch between the holes was 280 nm. The exposed e-beam resist was developed in anhydrous o-xylene (97 %, Sigma-Aldrich) for 45 s and then rinsed with IPA for 30 s. Subsequently, a 100 nm-thick TiO₂ layer was deposited at 90 °C to fill the e-beam resist nanoholes. To remove the TiO₂ layer that formed on top of the e-beam resist, the TiO₂ surface was maintained at 20 °C and etched by the reactive-ion etching (RIE) process using BCl₃ gas (40 sccm) and Ar gas (60 sccm), and source and stage powers of 500 W and 100 W, respectively. To prevent e-beam resist exposure, an O₂ plasma treatment was performed under an O₂ gas flow of 40 sccm at the room temperature, with a source power of 150 W and chamber pressure of 250 mTorr. To embed the TiO₂ nanodisc array into PDMS, a mixed solution of PDMS base resin and curing agent (Sylgard 184, Dow Corning Co.) was spin-coated onto the TiO₂ nanodisc array at a speed of 500 rpm for 3 min followed by annealing at 60 °C for 5 h. Subsequently, the cured PDMS with the TiO₂ nanodisc array was immersed in water for 10 h to dissolve the germanium oxide layer, and finally the PDMS-embedded TiO₂ nanodisc array was detached from the quartz substrate.

2.2 Optical characterization

Computer simulations of light propagating into the PDMS-embedded TiO₂ nanodisc arrays were performed using a commercial software package (FDTD Solution, Lumerical Inc. and FDTD Band Solver, Optiwave systems Inc.) to obtain the transmission and reflection spectra. The refractive index of TiO₂ used in the simulation was measured by ellipsometry (WVASE32, J.A. Woollam). For the optical simulation, a plane wave was injected onto the structure at a normal incidence with the electric field polarized along the x-axis. The x and y boundaries of the simulation domain were set with periodic boundary conditions. A perfectly matched layer at the z boundary of the domain was used, and simulations were performed with various unit cell sizes from 280 × 280 nm to 400 × 400 nm. Using a hyperspectral imaging microscope system (Horiba, XploRA), the reflection and transmission spectra of the samples were measured. To mechanically stretch the PDMS-embedded TiO₂ nanodisc arrays, a homemade radial stretching system was designed. This radial stretching system was equipped with 6 arms that would serve to hold and stretch the sample. Each arm featured a peg that moves along a curved track on a rotating frame, allowing the arms to be pulled apart in a synchronized and controlled manner. The arms are guided within a fixed frame that is situated between two rotating frames. As a result, the sample dimensions can be increased from its original size by about 43 % (from 6 mm up to 8.5 mm).

3.1 Key geometric parameter of TiO₂ metasurface: pitch

To simulate the optical properties of the TiO₂ metasurface, commercial software (Ansys Lumerical) was used to perform complete three-dimensional (3D) finite-difference time-domain (FDTD) analysis. First, an infinite array of TiO₂ nanodiscs completely embedded in PDMS was considered, as shown in Figure 1(a), and the effects of changing the geometric parameters of the array were investigated. A unit cell of a single TiO₂ nanodisc in the center with periodic boundary conditions in the x and y directions and a perfectly matched layer boundary in the z direction was used as the starting structure. A plane wave source with an electric field polarized along the x-axis and wave vector in the z direction was imposed onto the TiO₂ nanodisc side and then propagated through PDMS. The reflectance and transmittance spectra were obtained by field monitors above and below the structure. The simulated optical response of the array was mapped by changing three geometrical parameters: nanodisc height (H), nanodisc diameter (D), and array pitch (P). Additionally, the refraction indices of the substrates and nanodiscs were used as simulation parameters. The refractive index of TiO₂ used in the simulation was experimentally measured using a TiO₂ thin film deposited by atomic layer deposition (ALD) (Supplementary Figure S1), which was also used to form the metamaterial TiO₂ nanodiscs.

Figure 1:

Simulation results of TiO₂ nanodiscs completely embedded in uniform media with different indices. (a) Schematic of completely embedded TiO₂ nanodiscs for the optical simulation. (b) Simulated transmittance spectra of TiO₂ nanodiscs with different pitches and heights, at a fixed diameter of 120 nm. (c) Simulated transmittance spectra of TiO₂ nanodiscs with different pitches and diameters, at a fixed height of 275 nm. (d) Transmittances versus pitch of the completely embedded TiO₂ nanodiscs with a diameter of 120 nm and thickness of 275 nm.

The transmission resonances were simulated for different heights at a fixed diameter. This was repeated for different pitches, as shown in Figure 1(b). The heights were 225, 275, and 325 nm, and pitches were 280, 340, and 400 nm, while the diameter was fixed at 120 nm. The transmittance spectra exhibited sharp decrease at particular spectral locations (dips), which did not significantly shift with changes in H in the range of 275 ± 50 nm. In contrast, the dips significantly shifted with increasing array pitch from 280 to 400 nm. Subsequently, the diameter was varied (D = 110, 120, and 130 nm) at a fixed height of 275 nm, and the simulations were repeated at different pitches. The transmittance spectra are shown in Figure 1(c). From Figure 1(b) and (c), the location of the spectral dips depended strongly on the array pitch and weakly on the diameter and height of the nanodiscs. To evaluate the spectral dependence on pitch, a simulation was performed using a fine pitch sweep with P = 280–500 nm for nanodiscs with a diameter of 120 nm and height of 275 nm, as shown in Figure 1(d). The spectral location of the transmission bands exhibited redshifts with increasing pitch, and crossover at λ ∼ 295 nm. These results are consistent with data in the literature [29]. The locations of the scattering modes are controlled by the size and refractive index of the nanostructures, i.e., the Mie scattering cross sections, and it is essential to have high index material to exhibit resonances in the visible wavelengths. On the level of the resonating elements, the electric dipoles scatter light symmetrically in the plane transverse to the dipole axis, and the resonant magnetic dipole results from a coupling of incoming light to the circular displacement currents of the electric field, due to the field penetration and phase retardation inside the nanodiscs. It is well known that the geometric parameters (diameter and height) of the elements of the array influence the resonances. The collective optical resonances are sensitive to the change in the distance between the resonant nanostructures [36, 37]. This is a direct consequence to changes in the coupling between adjacent elements. This electromagnetic coupling enhances with decreasing the pitch [37], and in a large array of resonators, the nearest neighbors provide the strongest contribution to the overall resonances. The electromagnetic coupling is sensitive to changes in pitch between the scattering centers, and reducing this coupling leads to changes in resonance intensities [24, 39]. When the spacing between the scattering elements increased, the coupling is significantly reduced and then diminished, and the resonance spectra disappeared (Figure 1(d)). One of the resonances diminished at pitch values higher than ∼385 nm, and further increasing the pitch above 545 nm weakened the other resonance (Supplementary Figure S2). Thus, stretching PDMS can tune the transmission spectra because coupling is the main driver for spectral tuning.

3.2 Reducing the Rayleigh Anomaly diffraction

To elucidate the origin of the electromagnetic resonances A and B in Figure 1(d), FDTD simulations were used to obtain the electric and magnetic field distributions within the nanodiscs. For example, the field distributions for nanodiscs with P = 330 nm are shown in Figure 2(a)–(c). For resonance A, the electric field aligned along the direction of incident polarization (Figure 2(a) and (b)), whereas the magnetic field vector curls in the cross section (Y–Z plane) shown in Figure 2(c). For resonance B, the electric field vector curls in the cross section (X–Z plane) shown in Figure 2(e), and the magnetic field vector was perpendicular to the direction of incident polarization (Figure 2(d) and (f)). Therefore, A is the electric dipole resonance and B is the magnetic dipole resonance. Notably, when the resonances shifted with decreasing spacing, crossover of the electric dipole resonance was observed at shorter wavelengths than that of the magnetic dipole resonance (Supplementary Figure S3). In Figure 1(d), the Rayleigh anomaly (RA) diffraction was observed close to the Mie-lattice resonances [22, 40], [41], [42]. This diffraction originates from the periodic structure that serves as a thin transmission grating and diffracts the impinging light [43]. To utilize the Mie-lattice resonances for practical applications, it is essential to reduce the RA intensity. Therefore, we added another parameter in the design of the array by creating an optically asymmetric structure which affects the RA.

Figure 2:

Electric and magnetic field intensity plotted along the vertical TiO₂ nanodisc: (a)–(c) electric dipole resonance at λ = 502 nm and (d)–(f) magnetic dipole resonance at λ = 495 nm for the completely embedded TiO₂ nanodisc array with a pitch of 330 nm.

The general condition for the RA diffraction was described by Strutt [40].

where n _sub is the refractive index of the substrate, β _m is the diffraction angle in the substrate, n _sup is the refractive index of the superstrate, a _inc is the light angle in the superstrate, integer m is the order of the diffracted wave, λ is the wavelength of the light, and P is the pitch of the diffracting elements (the TiO₂ nanodiscs). Because the incident light is normal to the nanodisc array (along the z axis), a _inc is 0° and n _sub and n _sup are identical. When the angle β _m is 90°, the RA occurs due to the propagation of the diffracted wave parallel to the grating. Thus, for the geometry of our system, the first order diffraction grating Equation (1) becomes:

Equation (2) indicates that changing the optical index of the embedding medium shifts the spectral location of the RA resonance. For example, reducing the refractive index of the medium caused a blueshift in the RA resonance (Supplementary Figure S4), but the change in the index also shifts the dipole resonances. Subsequently, a metasurface with shifted RA diffraction was designed, which consists of an optically asymmetric structure in which the top and bottom surfaces of the TiO₂ nanodiscs are in contact with two media with different refractive indices (for example, PDMS and air). This structure was realized using partially embedded nanodiscs in PDMS. Figure 3(a) and (b) shows transmission and reflection when light was injected from the PDMS side, exhibiting a strong RA reflection. Figure 3(c) and (d) were obtained when light was injected from the air side, exhibiting a weak RA reflection. These results are attributed to the change in index at the interfaces. Because the effective index for the TiO₂-PDMS composite is approximately 1.6 and that of air is 1, when light is injected from the PDMS side and propagates through air, the index is significantly reduced (Δn = 0.6), which produces a strong reflection at the interface between the TiO₂-PDMS composite and air. Conversely, when light is injected from the air side, a smaller decrease in the index was observed Δn = 1.6–1.46 (the index of SiO₂) = 0.14, causing a weaker RA reflection.

Figure 3:

Asymmetric media structure of partially embedded TiO₂ nanodiscs in PDMS with a diameter of 120 nm and thickness of 275 nm for Rayleigh anomaly resonance. (a) Transmittance and (b) reflectance spectra versus pitch of the TiO₂ nanodiscs with light injected from the PDMS side and transmitted through air. (c) Transmittance and (d) reflectance spectra versus pitch of the TiO₂ nanodiscs with light injected from air and transmitted through PDMS. Insets of panel (c) and (d) show the schematics of simulated TiO₂ nanodisc structures.

3.3 Fabrication of dynamically tunable TiO₂ metasurface

The dynamic tuning of the TiO₂ nanodisc color filtering system was realized experimentally by mechanically stretching PDMS with the partially embedded TiO₂ nanodiscs. Stamping methods had been used to transfer nanostructures into flexible substrates [44, 45]. These transfers may form defects in the nanopattern, which reduces device fidelity. As shown in Figure 4, a different fabrication method for embedding TiO₂ nanodiscs in PDMS was designed to produce defect-free structures. A sacrificial layer of GeO _x film, which can be dissolved in water, was deposited onto a glass substrate. This layer was coated with an electron-beam resist film and patterned by electron-beam lithography to produce a nanohole array. Subsequently, the nanoholes were filled with TiO₂ using ALD, which has excellent step coverage. Near-perfect coverage was confirmed by evaluating a filled nano-trench (Figure S5). As expected, filling the nanoholes resulted in a thin TiO₂ film on the electron-beam resist, which was completely removed by reactive ion etching. Thus, the height of TiO₂ nanodiscs was determined by the electron-beam resist thickness. Therefore, the electron-beam resist was selectively etched by O₂ plasma treatment to form a TiO₂ nanodisc array on the GeOx layer. The use of a dry lift-off step provided a defect-free TiO₂ metasurface. Subsequently, a PDMS solution was poured onto the TiO₂ nanodiscs and cured. Finally, the device was immersed in water to remove the GeO _x layer. The combination of the lift-off step and sacrificial layer produces a defect-free stretchable metasurface. The scanning electron microscopy (SEM) image of as-fabricated TiO₂ nanodiscs is shown in Figure S6.

Figure 4:

Fabrication process of PDMS-embedded TiO₂ nanodisc array-based color filters.

3.4 Experimental demonstration of magnetic dipole resonances

The transmittance spectra of the metasurface were measured using a commercial hyperspectral imaging system. By mechanically stretching the PDMS, the pitch between the TiO₂ nanodiscs was dynamically changed from 280 to 380 nm. Figure 5(a) shows spectra redshift with increasing pitch similar to the simulation results in Figure 1(d). For comparison, Figure 5(b) shows the simulated spectra of the metasurface dimensions, which corresponds with the experimental results, exhibiting a similar redshift trend. However, the simulated bands were much narrower with transmission minima of <10 % than the experiment ones, which exhibited broader transmission bands with minima of >30 %. Additionally, a single dip was observed in the experimental spectra, whereas the simulated spectra showed double dips representing the electric and magnetic dipole resonances. These differences are commonly reported for dielectric metasurface arrays [29, 30, 35] but the fact that often only one broad dip is observed remains unresolved. It is crucial to understand the origin of these differences to achieve the theoretical near-zero transmissions and be able to obtain high-quality resonances.

Figure 5:

Dynamic color tuning by stretching PDMS-embedded TiO₂ nanodiscs: (a) experimental and (b) simulated transmittance spectra of PDMS-embedded TiO₂ nanodiscs with different pitches from 280 to 380 nm. The Insets in panel (a) show the optical microscopy images of PDMS-embedded TiO₂ nanodiscs with different pitches from 280 to 380 nm. Transmittance spectra (c) and (d) for PDMS-embedded TiO₂ nanodiscs and (e) and (f) for PMMA-coated TiO₂ nanodiscs on glass substrate at a pitch of 280 and 340 nm – non-averaged simulated spectrum (blue line), simulated spectrum from averaged spectra with various angles of incident light (red line), and experimental spectrum (green line). The insets in panel (c)–(f) show the schematics of the TiO₂ nanodiscs with different media.

We suggest two points to investigate: (1) the origin of the differences between the computer simulations and experimental setups, and (2) the effect of the presence of slight variations in the array pitch and also the possibility of surface non-uniformity caused by the PDMS transfer or handling. For the former, an ideal case with a plane wave injection at a normal incidence was used in the simulations, whereas a light injection angle set by the numerical aperture (NA) of the objective lens was used experimentally. The experimental objective lens had NA = 0.13, which corresponds to a half angle of incidence equivalent to ±7.4° relative to the normal incidence. It is recognized that the transmission spectra of periodic dielectric nanostructures are dependent on the incidence angle [17, 24]. When the transmission spectra are averaged over the incidence angle, the resonance band broadening is reasonable. This was investigated by performing FDTD simulations in the incident angle range of 82.6°–97.4° with 0.3° steps. The simulated spectra with different incident angles are shown in Figure S7. A shift in the resonance position was observed with changes in polar angle (θ) and azimuthal angle (φ). The simulated data were averaged and plotted (in red) in Figure 5(c) with the transmission spectrum of the ideal case (plotted in blue) at a normal incidence for PDMS-embedded TiO₂ nanodiscs with P = 280 nm. The averaged spectra exhibited a much less transmission minimum (38 %) than that at a normal incidence which were about 8 %. Notably, the averaged spectra exhibited overlapping spectra dips, which correspond with the experimental spectrum (Figure 5(c), plotted in green). A similar spectrum was obtained at P = 340 nm as shown in Figure 5(d). The transmission minimum is reduced for the angle averaged simulated plots compared with the normal incidence simulated plots, as shown in Figure 5(c) and (d). The weaker spectra dips in Figure 5(a) are due to the NA (0.13) of the objective lens in experiment compared with the normal incidence simulation in Figure 5(b).

The second hypothesis, which attributes the differences between experimental and simulated results to slight variations in the spatial dimensions during device fabrication was also investigated. Spatial variations and surface non-uniformity can occur during the (a) transfer of the TiO₂ metasurface to PDMS or (b) mounting of the thin flexible metasurface onto the mechanical stretching mount. Furthermore, these non-uniformities can be amplified by the stretching process. A small local variation in the position of the array elements may cause incoherency in strongly coupled modes, resulting in broader collective resonance. To investigate this hypothesis, TiO₂ nanodiscs were formed on a rigid glass substrate to eliminate bending, twisting, or variations in the pitch between the nanodiscs during the transfer process. A structure similar to PDMS-embedded TiO₂ metasurface was implemented by fabricating the TiO₂ metasurface on a glass substrate and embedding the metasurface in a polymethyl methacrylate (PMMA) acrylic glass with a thickness equal to the nanodisc height. The refractive index of PMMA is approximately 1.48, which is close to that of PDMS (n = 1.46), and thus the two systems are similar. The low viscosity of the PMMA solution enabled easy filling between the TiO₂ nanodiscs by spin coating. The dipole resonances of the PMMA-containing structure were simulated at a normal incidence and incident light with different angles. Figure 5(e) shows the simulated transmittance spectrum at a normal incidence (blue) and averaged transmittance spectra with different angles (red) for the PMMA-coated TiO₂ metasurface on the glass substrate (P = 280 nm). The averaged spectra of the glass/PMMA metasurface exhibited a similar trend with overlapping bands. It was experimentally confirmed that the spectra (green in Figure 5(e)) for the glass/PMMA metasurface at P = 280 nm resembles the simulation spectra obtained with illumination angle averaged (red in Figure 5(e)) for this geometry. Notably, for the glass/PMMA metasurface (green in Figure 5(e)), the double transmission dips were experimentally observed and resemble those in the simulation. In addition, the measured dip was sharper with a full width at half maximum (FWHM) of 7.2 nm, compared to the case of metasurface embedded in PDMS (green in Figure 5(c)) with FWHM = 9.0 nm. Subsequently, as shown in Figure 5(f), the pitch was increased to 340 nm, and the experimental data (in green) for the electric and magnetic dipole resonances show two distinct dips which are similar to the case for the normal incidence light in the averaged simulated spectra. Based on these results, we concluded that the illumination angle variations strongly influence the intensities of the transmission dips. Moreover, the spatial non-uniformity induced in the metasurface during the mechanical stretching causes band broadening due to pitch variations. The measured FWHM of the spectra of the glass/PMMA metasurface is 3.4 nm (green in Figure 5(f)) was larger than that of the averaged simulation (red in Figure 5(f)), which has FWHM = 2.1 nm.

According to Figure 5(c)–(f), we concluded that pitch variation during mechanically stretching of the PDMS is likely more dominant for broadening the experimental spectra. However, these variations do not negatively affect the functionality of the metasurface as a narrow-band tunable filter for the dynamic selection of visible wavelengths. To accurately control the pitch of the PDMS-embedded TiO₂ nanodiscs, a stretching system is being developed using dielectric elastomer actuators [46] instead of a mechanical force. Using the dielectric elastomer actuators, it is possible to stretch along the radial direction and control the stretching electrically. Thus, a more uniform and accurate control of nanodisc array pitch is expected, which may produce narrow-band TiO₂ nanodisc color filters.